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Skewness Formula:
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Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. It describes the extent to which a distribution differs from a normal distribution in terms of symmetry.
The calculator uses the skewness formula:
Where:
Explanation: The third central moment measures the lopsidedness of the distribution, while dividing by the cube of standard deviation makes the measure dimensionless and scale-invariant.
Details: Skewness is crucial in statistics for understanding the shape of data distributions. It helps identify whether data is symmetric, left-skewed (negative skew), or right-skewed (positive skew), which affects statistical analyses and modeling decisions.
Tips: Enter the third central moment and standard deviation values. Both values must be valid (standard deviation > 0). The result is a dimensionless measure of skewness.
Q1: What do different skewness values indicate?
A: Skewness = 0 indicates symmetric distribution; > 0 indicates right-skewed (tail on right); < 0 indicates left-skewed (tail on left).
Q2: What are typical ranges for skewness?
A: For normal distributions, skewness is near 0. Values between -0.5 and 0.5 indicate approximately symmetric data, while values beyond ±1 show highly skewed distributions.
Q3: How is the third central moment calculated?
A: μ₃ = E[(X - μ)³], where E is the expected value operator, X is the random variable, and μ is the mean of the distribution.
Q4: Are there alternative skewness measures?
A: Yes, Pearson's first and second skewness coefficients, Bowley's measure, and sample skewness with adjustments for bias are commonly used alternatives.
Q5: When is skewness particularly important?
A: Crucial in finance (asset returns), quality control, environmental studies, and any field where distribution shape affects conclusions and decisions.